【正文】 現(xiàn)狀 ...............................................................................................................1 形態(tài)學(xué)的研究目的和意義 ...................................................................................................2 第 2 章 形態(tài)學(xué)基本理論 ....................................................................................................................4 形態(tài)學(xué)的研究?jī)?nèi)容 ...............................................................................................................4 二值圖像形態(tài)學(xué) ...................................................................................................................5 數(shù)字圖像的表示及反射平移 ....................................................................................5 二值圖像的腐蝕和膨脹運(yùn)算 ....................................................................................6 二值形態(tài)膨脹和腐蝕運(yùn)算的性質(zhì) ............................................................................8 二值圖像開(kāi)運(yùn)算和閉運(yùn)算 ........................................................................................9 二值圖像開(kāi)閉運(yùn)算性質(zhì) ..........................................................................................10 灰度圖像形態(tài)學(xué) ................................................................................................................. 11 灰度形態(tài)學(xué)理論基礎(chǔ) .............................................................................................. 11 灰度形態(tài)學(xué)腐蝕和膨脹運(yùn)算 ..................................................................................12 灰度形態(tài)學(xué)腐蝕和膨脹運(yùn)算性質(zhì) ..........................................................................15 灰度形態(tài)學(xué)開(kāi)運(yùn)算和閉運(yùn)算 ..................................................................................16 灰度形態(tài)學(xué)開(kāi)運(yùn)算和閉運(yùn)算性質(zhì) ..........................................................................17 軟數(shù)學(xué)形態(tài)學(xué) .....................................................................................................................18 模糊數(shù)學(xué)形態(tài)學(xué) .................................................................................................................18 第 3 章 形態(tài) 學(xué)在圖像處理的基本應(yīng)用 ..........................................................................................19 擊中或擊不中變換 .............................................................................................................19 細(xì)化和粗化 .........................................................................................................................19 形態(tài)學(xué)重構(gòu) .........................................................................................................................20 形態(tài)學(xué)圖像平滑 .................................................................................................................21 圖像的骨架化及邊界像素值的測(cè)定 .................................................................................23 第 4 章 基于形態(tài)學(xué)的圖像邊緣檢測(cè) ..............................................................................................24 圖像邊緣的定義 .................................................................................................................24 理工大學(xué)畢業(yè)論文 4 結(jié)構(gòu)元素的確定 .................................................................................................................24 結(jié)構(gòu)元素的形狀 ......................................................................................................25 結(jié)構(gòu)元素的尺寸 ......................................................................................................25 形態(tài)學(xué)算法和傳統(tǒng)算法的邊緣檢測(cè)比較 .........................................................................26 基于單尺度單結(jié)構(gòu)的抗噪型形態(tài)學(xué)邊緣檢測(cè) .................................................................30 基于多尺度單結(jié)構(gòu)的邊緣檢測(cè) .........................................................................................32 基于單尺度多結(jié)構(gòu)的邊緣檢測(cè) .........................................................................................34 基于多尺度多結(jié)構(gòu)的邊緣檢測(cè) .........................................................................................35 結(jié)論 ....................................................................................................................................................36 參考文獻(xiàn) ............................................................................................................................................37 附錄 Ⅰ 外文文獻(xiàn)翻譯 ......................................................................................................................38 附錄 Ⅱ 程序清單 ..............................................................................................................................68 致謝 ....................................................................................................................................................76 理工大學(xué)畢業(yè)論文 1 第 1 章 緒論 形態(tài)學(xué)的研究現(xiàn)狀 數(shù)學(xué)形態(tài)學(xué)歷史可回溯到 19世紀(jì)的 Eular,Steiner Crofton和本世紀(jì)的 Minkowski, Matheron和 Serra。 關(guān)鍵詞 ：形態(tài)學(xué)；圖像處理；邊緣檢測(cè) 理工大學(xué)畢業(yè)論文 2 Abstract Mathematical morphology founded on set theory is a new method applied in the field of image processing and pattern recognition. Its prime principle is using a certain structuring element to measure and extract the corresponding form in an image so that we can analyze and recognize the image. This paper focusing on the mathematical morphology image processing method introduces the morphological applications in hit or miss transform, image of refinement and coarsening, image reconstruction, image smoothing, focuses on a variety of morphological image edge detection algorithm to do the simulation experiments, and pares to the traditional edge detection algorithm. Finally the results will be analyzed. Keywords： morphology。 UNIVERSITY OF TECHNOLOGY 畢業(yè)論文 題 目 基于形態(tài)學(xué)圖像處理方法研究 學(xué)生姓名 學(xué) 號(hào) 專業(yè)班級(jí) 通信工程 指導(dǎo)教師 學(xué) 院 計(jì)算機(jī)與通信 答辯日期 2021 年 基于形態(tài)學(xué)圖像處理方法研究 Research on image processing method on morphology xxx 理工大學(xué)畢業(yè)論文 1 摘 要 數(shù)學(xué)形 態(tài)學(xué)是一種基于集合論的方法和理論， 它 的基本思想是